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Scientific Measurements. Objective I. Convert measurements to scientific notation. As a group, list as many measurements you can. Scientific Notation. exponential form a number is written as the product of 2 numbers a coefficient and 10 raised to a power 3.2 x 10 9.

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## Scientific Measurements

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**Scientific Measurements**Objective I. Convert measurements to scientific notation As a group, list as many measurements you can.**Scientific Notation**exponential form • a number is written as the product of 2 numbers a coefficient and 10 raised to a power 3.2 x 109**Coefficient** is always a number greater than or equal to one and less than 10 • The exponent indicates how many times the coefficient must be multiplied by 10 to equal the standard number Ex: 8.4 x 104 = 8.4 x 10 x 10 x 10 x 10 = 84,000**Writing numbers greater than 10 in scientific notation**Move the decimal all the way to the left until you only have one number on the left side of the decimal. ex: 6,000,000 6.000000 Count how many places you moved the decimal 6 You will write the whole number, decimal, 1 zero 6.0 Next, you will place an x (times), then the base 10 with an exponent. The exponent will be the number of spaces you moved the decimal. 6.0 x 106**Practice**= 6.2 x 104 = 3.45 x 108 = 8.7 x 1010 = 6.452 x 103 62,000 345,000,000 87,000,00000 6452**What if the number is not a whole number (number less than**10 to start with? • These numbers will be written with a negative exponent. • You will move the decimal to the right this time. Still count the places you moved. You will also still have 1 whole number on the left of the decimal. • Ex: .00000000458 • 000000004.58 • Count how many places you moved the decimal • 9 • Drop the numbers before the 4 (they are not significant) • 4.58 • Now write this number with your base 10 and exponent • 4.58 x 10-9**REMEMBER!!!!**• If you move decimal , the exponent will be negative • If you move decimal , the exponent will be positive**More practice**• 98,090,000 • 789000 • .0098 • .000008 = 9.809 x 107 = 7.89 x 105 = 9.8 x 10-3 = 8 x 10-6**Scientific notation to standard form**• 8.3 x 104 Move the decimal 4 places to the right. 8.3 x 10-4 Move the decimal 4 places to the left • Try these! • 2.0 x 105 200,000 • 5.6 x 10-4 .00056**Accuracy vs Precision**• Measurements should be both correct and reproducible. • Quite different • Accuracy- how close a measurement comes to the actual or true value of whatever is measured. • Precision- how close a series of measurements are to one another.**A**B B C**ERROR???**• Water boils at 100oC • LAB= WATER BOILED AT 99.10C • WHAT HAPPENED? • ERROR = EXPERIMENTAL VALUE – ACCEPTED VALUE • Percent error=IerrorI X 100% Accepted value % error= I99.1 – 100.0I x 100% 100.0 = 0.9/100.0 x 100% = 0.009 x 100% = 0.9%**THINK!!!**• If you look back at almanacs, olympic track records were recorded differently. • From 1948 to 1999 they were recorded to the nearest tenth (9.5), but since 2000 they are recorded to the nearest hundredth (9.49) • Why do you think more recently recorded race times contain more digits to the right of the decimal?**Significant Numbers (digits)**Include all digits know plus last estimated digit.**Calculating with Significant digits**• A calculated answer cannot be more precise than the least precise measurement from which it was calculated • Don’t round your answers until you figure out the number of significant digits to use • Round to the correct # of significant numbers, then apply rules for expressing number in scientific notation.**Significant figures in addition**ADD: 12.52 349.0 + 8.24 __________ 369.76= 369.8 or 3.698 x 102 • Align the decimal points and add the numbers • Round the answer to match the measurement with the least number of decimal places. • 349.0 has the least sig. fig. to the right (1). So, we must round out answer to one place past decimal**Practice**61.2 + 9.35 + 8.6 = 9.44 – 2.11 = 34.61 - 17.3**Multiplication & Division**• Round the answer the the same number of significant numbers as the measurement with the least number of significant digits. • Ex: 7.55 x 0.34 = 2.567 • 0.34 only has 2 sig. fig. so we round our answer so it only has 2. • 2.567 = 2.6**a) 2.10 x 0.70 =b) 2.4526 / 8.4 =c) 8.3 x**2.22 =d) 8432 / 12.5 =e) 22.4 m x 11.3 m x 5.2 m =**Quick lab**P. 72

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